The officers were killed as they were travelling in two buses which came under attack from armed men close to the town of Rafiah, on the Gaza border. As a result of the attack, Egypt closed down the Rafiah crossing between the Sinai Peninsula and Gaza.

Hamas, an offshoot of the Muslim Brotherhood, enjoyed close ties to Islamist President Mohammed Morsi and has been “feeling the heat” from Egypt's new army-backed leadership, which deposed Morsi last month.

Cairo accused Hamas of interfering in Egyptian affairs and encouraging the terrorist activity in the lawless Sinai.

"The Palestinian people, the people of Gaza, must not pay the price for any problems or differences inside Egypt," Ghazi Hamad, deputy foreign minister of the Hamas-run government said, according to Reuters.

"Gaza people have enough problems. This crossing should be named the crossing of humiliation and not Rafiah," Mai Jarada, a business student in Tunisia who attended a wedding in Gaza and now cannot leave the territory, told Reuters.

At a news conference on Wednesday, Hamad rejected accusations by some Egyptian officials that Hamas had intervened on Morsi's behalf during violence in Egypt.

If the tension with the Egyptian army has not been enough, the new Gaza branch of the group Tamarod has continued broadcasting messages against the Hamas leadership. “Tamarod” (“Rebel”) is the name of the popular anti-Islamist youth movement which led popular protests against Morsi in the run up to his removal by the military; its Gaza branch has focused on ousting the Muslim Brotherhood-linked Hamas.

The group has released a statement accusing Hamas of murder, torture, bribes and smuggling. “Those who carry resistance fighters’ rifles must stop also pointing those rifles at their own people,” the group accused.